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  • 2 years ago

EXPAND sqrt{/frac{1-x}{1+x}}

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  1. Calculator
    • 2 years ago
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    \[\Huge \sqrt{\frac{1-x}{1+x}}\]

  2. Calculator
    • 2 years ago
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    up to power x^2

  3. Calculator
    • 2 years ago
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    i get \[1-x+\frac{x^2}{2} - \frac{x^3}{8} - \frac{3x^4}{64}\]

  4. Calculator
    • 2 years ago
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    @saifoo.khan

  5. Calculator
    • 2 years ago
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    wolfram got \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

  6. saifoo.khan
    • 2 years ago
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    Unfortunately i forgot the formula! D:

  7. wio
    • 2 years ago
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    Is it a maclaurin series?

  8. Calculator
    • 2 years ago
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    you can try that

  9. wio
    • 2 years ago
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    I want to know what is meant by Expand, since that's the only thing that comes to mind.

  10. Calculator
    • 2 years ago
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    you can use this \[(x+a)^n=\sum ^{n}_{ k=0} \left(\begin{matrix}n \\ k\end{matrix}\right) x^k a^{(n-k)}\]

  11. Calculator
    • 2 years ago
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    or \[(1+x)^n = 1+nx+\frac{(n)(n-1)}{2!}(x^2)+...\]

  12. wio
    • 2 years ago
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    That works for \(n\in \mathbb{N}\).

  13. wio
    • 2 years ago
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    In this case you have a square root...

  14. Calculator
    • 2 years ago
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    still can, watch

  15. Calculator
    • 2 years ago
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    \[\sqrt{\frac{1-x}{1+x}} \\ \\ \frac{\sqrt{1-x}}{\sqrt{1+x}} \\ \\ (1-x)^\frac{1}{2}(1+x)^{-\frac{1}{2}}\]

  16. Calculator
    • 2 years ago
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    expand separately

  17. Calculator
    • 2 years ago
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    mix them by multiplying together

  18. wio
    • 2 years ago
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    Yeah, my problem is with \(1/2 \notin \mathbb{N}\)

  19. Calculator
    • 2 years ago
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    I don't think it should be natural number

  20. Calculator
    • 2 years ago
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    i mean real number will do

  21. wio
    • 2 years ago
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    How can you have summations or binomial coefficients with rational numbers?

  22. amoodarya
    • 2 years ago
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    interval of x is ?

  23. Calculator
    • 2 years ago
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    the formula list says can use

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  24. Calculator
    • 2 years ago
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    we use the second one (1+x)^n

  25. Calculator
    • 2 years ago
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    http://en.wikipedia.org/wiki/Binomial_series look at the History section

  26. amoodarya
    • 2 years ago
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    |dw:1359798673882:dw|

  27. amoodarya
    • 2 years ago
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    |dw:1359798819059:dw|

  28. Calculator
    • 2 years ago
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    or maybe its \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

  29. Calculator
    • 2 years ago
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    hmm

  30. Calculator
    • 2 years ago
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    based from the formula as long as its in the from ("1"+x)^n should be fine to expand, i tried it

  31. Calculator
    • 2 years ago
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    from \[(1-x)^{1/2} \\ \\ n=-1/2, x=-x(for formula) \\ \\ [1-\frac{x}{2}+\frac{(\frac{1}{2})(\frac{1}{2}-1)}{2}(x^2)] \\ \\ 1-\frac{x}{2}-\frac{x^2}{8}\]

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